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Block #115,769

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/13/2013, 11:56:42 PM Β· Difficulty 9.7454 Β· 6,708,945 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
34ac26f4c2b9d293024230d2249f14d4548c7c43b581f16ade887726e654a242
View on Chainz β†—

Height

#115,769

Difficulty

9.745449

Transactions

1

Size

200 B

Version

2

Bits

09bed5bc

Nonce

1,646,043

Timestamp

8/13/2013, 11:56:42 PM

Confirmations

6,708,945

Mined by

⛏️ P2SHAdhZ7LCo5gNnWSknME6vrwhUyCjsXbkNWv

Merkle Root

cfae056f593220701ed9fe446b1350dc38e0773f756627b1bd0a759cd3d016fa
Transactions (1)
Coinbasecfae056f593220…0a759cd3d016fa
1 in β†’ 1 out10.5100 XPM109 B
AdhZ7LCo…jsXbkNWv
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.

3.752 Γ— 10⁹⁢(97-digit number)
37521419413302460284…79969097954391262249
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
3.752 Γ— 10⁹⁢(97-digit number)
37521419413302460284…79969097954391262249
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.752 Γ— 10⁹⁢(97-digit number)
37521419413302460284…79969097954391262251
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
7.504 Γ— 10⁹⁢(97-digit number)
75042838826604920569…59938195908782524499
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.504 Γ— 10⁹⁢(97-digit number)
75042838826604920569…59938195908782524501
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
1.500 Γ— 10⁹⁷(98-digit number)
15008567765320984113…19876391817565048999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.500 Γ— 10⁹⁷(98-digit number)
15008567765320984113…19876391817565049001
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
3.001 Γ— 10⁹⁷(98-digit number)
30017135530641968227…39752783635130097999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.001 Γ— 10⁹⁷(98-digit number)
30017135530641968227…39752783635130098001
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
6.003 Γ— 10⁹⁷(98-digit number)
60034271061283936455…79505567270260195999
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:57,841,778 XPMΒ·at block #6,824,713 Β· updates every 60s
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