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Block #1,084,121

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/31/2015, 9:06:12 AM Β· Difficulty 10.7711 Β· 5,725,691 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
045d029d3d3d69e940f950b99be7e86a80fe056527ea77a42ea6a26fab3bb647
View on Chainz β†—

Height

#1,084,121

Difficulty

10.771113

Transactions

2

Size

84.26 KB

Version

2

Bits

0ac567b1

Nonce

524,296,399

Timestamp

5/31/2015, 9:06:12 AM

Confirmations

5,725,691

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

64a242fdc9266ebd46c92fe33fe74aaf53bf232d5de151d90d62f9c77b240328
Transactions (2)
Coinbase4f979bcf8e6b3e…5e7083553d395a
1 in β†’ 1 out9.4900 XPM116 B
ANSXnLY2…Sd25TjkD
e5351182a5115a…e34d32938e2f36
581 in β†’ 2 out4500.0100 XPM84.06 KB
Ae5WFHbn…gBo7rvHrAH2eSzNP…SCBCTjp2
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.066 Γ— 10⁹⁡(96-digit number)
20660546922622846687…14593911099844835119
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.066 Γ— 10⁹⁡(96-digit number)
20660546922622846687…14593911099844835119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.066 Γ— 10⁹⁡(96-digit number)
20660546922622846687…14593911099844835121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
4.132 Γ— 10⁹⁡(96-digit number)
41321093845245693375…29187822199689670239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.132 Γ— 10⁹⁡(96-digit number)
41321093845245693375…29187822199689670241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
8.264 Γ— 10⁹⁡(96-digit number)
82642187690491386751…58375644399379340479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.264 Γ— 10⁹⁡(96-digit number)
82642187690491386751…58375644399379340481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.652 Γ— 10⁹⁢(97-digit number)
16528437538098277350…16751288798758680959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.652 Γ— 10⁹⁢(97-digit number)
16528437538098277350…16751288798758680961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.305 Γ— 10⁹⁢(97-digit number)
33056875076196554700…33502577597517361919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.305 Γ— 10⁹⁢(97-digit number)
33056875076196554700…33502577597517361921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.611 Γ— 10⁹⁢(97-digit number)
66113750152393109401…67005155195034723839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,722,579 XPMΒ·at block #6,809,811 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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