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Block #72,491

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 12:31:07 AM Β· Difficulty 8.9941 Β· 6,754,811 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
030b7fffee48bc3c3e90f1391e48337a0ea7e773781c58566e4bee0065207b1e
View on Chainz β†—

Height

#72,491

Difficulty

8.994106

Transactions

1

Size

198 B

Version

2

Bits

08fe7db8

Nonce

176

Timestamp

7/21/2013, 12:31:07 AM

Confirmations

6,754,811

Mined by

⛏️ P2SHAH7Eh9GYMSnm23owcXVdfkeuiPK86X1CDg

Merkle Root

f4690c896e978c7921a6d20ade6ab9221e4d941e7ee4b125711d542cca4517f3
Transactions (1)
Coinbasef4690c896e978c…1d542cca4517f3
1 in β†’ 1 out12.3400 XPM110 B
AH7Eh9GY…K86X1CDg
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.

2.302 Γ— 10⁹⁰(91-digit number)
23021971870382699417…27674022024925228499
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
2.302 Γ— 10⁹⁰(91-digit number)
23021971870382699417…27674022024925228499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.302 Γ— 10⁹⁰(91-digit number)
23021971870382699417…27674022024925228501
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
4.604 Γ— 10⁹⁰(91-digit number)
46043943740765398835…55348044049850456999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.604 Γ— 10⁹⁰(91-digit number)
46043943740765398835…55348044049850457001
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
9.208 Γ— 10⁹⁰(91-digit number)
92087887481530797671…10696088099700913999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.208 Γ— 10⁹⁰(91-digit number)
92087887481530797671…10696088099700914001
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
1.841 Γ— 10⁹¹(92-digit number)
18417577496306159534…21392176199401827999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.841 Γ— 10⁹¹(92-digit number)
18417577496306159534…21392176199401828001
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
3.683 Γ— 10⁹¹(92-digit number)
36835154992612319068…42784352398803655999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,862,527 XPMΒ·at block #6,827,301 Β· updates every 60s
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