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Block #920,543

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/3/2015, 1:37:19 AM Β· Difficulty 10.9178 Β· 5,887,486 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b6885e2ae5901f023eea26e643a4722a308c0fe525fda01758372de45b06cb00
View on Chainz β†—

Height

#920,543

Difficulty

10.917776

Transactions

2

Size

433 B

Version

2

Bits

0aeaf365

Nonce

1,981,568,294

Timestamp

2/3/2015, 1:37:19 AM

Confirmations

5,887,486

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5f3819de957fd66f9ded8dee52e50b6c8dc0947d6e8a58f4db45de158eb0aeea
Transactions (2)
Coinbasee29c22934e3c2a…ad9902a8704fc6
1 in β†’ 1 out8.3900 XPM116 B
ANSXnLY2…Sd25TjkD
18fd3294457464…4c54d9d06f1e9e
1 in β†’ 2 out4.3500 XPM226 B
AHDvNdeo…inoYUzzzARMQTG3g…Ee4c1PVA
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.

3.279 Γ— 10⁹⁷(98-digit number)
32798311497374849838…43629311132671672959
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
3.279 Γ— 10⁹⁷(98-digit number)
32798311497374849838…43629311132671672959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.279 Γ— 10⁹⁷(98-digit number)
32798311497374849838…43629311132671672961
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
6.559 Γ— 10⁹⁷(98-digit number)
65596622994749699677…87258622265343345919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.559 Γ— 10⁹⁷(98-digit number)
65596622994749699677…87258622265343345921
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
1.311 Γ— 10⁹⁸(99-digit number)
13119324598949939935…74517244530686691839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.311 Γ— 10⁹⁸(99-digit number)
13119324598949939935…74517244530686691841
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
2.623 Γ— 10⁹⁸(99-digit number)
26238649197899879871…49034489061373383679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.623 Γ— 10⁹⁸(99-digit number)
26238649197899879871…49034489061373383681
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
5.247 Γ— 10⁹⁸(99-digit number)
52477298395799759742…98068978122746767359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.247 Γ— 10⁹⁸(99-digit number)
52477298395799759742…98068978122746767361
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
1.049 Γ— 10⁹⁹(100-digit number)
10495459679159951948…96137956245493534719
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:57,708,276 XPMΒ·at block #6,808,028 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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