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Block #79,607

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/23/2013, 2:45:31 PM Β· Difficulty 9.2437 Β· 6,716,787 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4ea072250bc7b9b0917ad2bec434a8dca69dfde9a2c0a6493ed83774e0c6d10d
View on Chainz β†—

Height

#79,607

Difficulty

9.243713

Transactions

1

Size

200 B

Version

2

Bits

093e6400

Nonce

537

Timestamp

7/23/2013, 2:45:31 PM

Confirmations

6,716,787

Mined by

⛏️ P2SHAYZKkgwtsty852heqw6tj9J9GRQQkmaD2C

Merkle Root

9b3f9436b58e96925b3d5ef41e4c0479f809b06dccaa1f3092adb59e04675343
Transactions (1)
Coinbase9b3f9436b58e96…adb59e04675343
1 in β†’ 1 out11.6900 XPM110 B
AYZKkgwt…QQkmaD2C
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.

1.541 Γ— 10⁹⁡(96-digit number)
15410004165700840892…88149843058369560959
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
1.541 Γ— 10⁹⁡(96-digit number)
15410004165700840892…88149843058369560959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.541 Γ— 10⁹⁡(96-digit number)
15410004165700840892…88149843058369560961
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
3.082 Γ— 10⁹⁡(96-digit number)
30820008331401681785…76299686116739121919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.082 Γ— 10⁹⁡(96-digit number)
30820008331401681785…76299686116739121921
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
6.164 Γ— 10⁹⁡(96-digit number)
61640016662803363571…52599372233478243839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.164 Γ— 10⁹⁡(96-digit number)
61640016662803363571…52599372233478243841
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
1.232 Γ— 10⁹⁢(97-digit number)
12328003332560672714…05198744466956487679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.232 Γ— 10⁹⁢(97-digit number)
12328003332560672714…05198744466956487681
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
2.465 Γ— 10⁹⁢(97-digit number)
24656006665121345428…10397488933912975359
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:57,615,149 XPMΒ·at block #6,796,393 Β· updates every 60s
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