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Block #708,584

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2014, 7:02:21 PM Β· Difficulty 10.9574 Β· 6,102,247 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
98be0890398231932bb0720e429a55c42e18d9bf532fedbcac25faa9178e284f
View on Chainz β†—

Height

#708,584

Difficulty

10.957436

Transactions

2

Size

2.87 KB

Version

2

Bits

0af51a86

Nonce

2,323,184,136

Timestamp

9/5/2014, 7:02:21 PM

Confirmations

6,102,247

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2308e33cf6c523c614451e19d26aa8c3fe486c486b8dd2112928111775d4a9f7
Transactions (2)
Coinbaseb9abc6a1ac15ac…9eff59ecca234e
1 in β†’ 1 out8.3500 XPM116 B
ANSXnLY2…Sd25TjkD
be012f4443fcba…8f750268fbd279
18 in β†’ 2 out1785.3222 XPM2.67 KB
AMFz2Lqz…RzqfazbyAWnAimL4…MAkR7ukp
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.

2.359 Γ— 10⁹⁡(96-digit number)
23596217788810319185…37241875561299404799
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
2.359 Γ— 10⁹⁡(96-digit number)
23596217788810319185…37241875561299404799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.359 Γ— 10⁹⁡(96-digit number)
23596217788810319185…37241875561299404801
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
4.719 Γ— 10⁹⁡(96-digit number)
47192435577620638370…74483751122598809599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.719 Γ— 10⁹⁡(96-digit number)
47192435577620638370…74483751122598809601
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
9.438 Γ— 10⁹⁡(96-digit number)
94384871155241276740…48967502245197619199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.438 Γ— 10⁹⁡(96-digit number)
94384871155241276740…48967502245197619201
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
1.887 Γ— 10⁹⁢(97-digit number)
18876974231048255348…97935004490395238399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.887 Γ— 10⁹⁢(97-digit number)
18876974231048255348…97935004490395238401
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
3.775 Γ— 10⁹⁢(97-digit number)
37753948462096510696…95870008980790476799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.775 Γ— 10⁹⁢(97-digit number)
37753948462096510696…95870008980790476801
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
7.550 Γ— 10⁹⁢(97-digit number)
75507896924193021392…91740017961580953599
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:57,730,743 XPMΒ·at block #6,810,830 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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