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Block #115,501

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/13/2013, 7:43:19 PM Β· Difficulty 9.7447 Β· 6,679,308 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c6265ea8149994f43079799589be6bed07084afa0526a70e9fc30dcb1b9975c0
View on Chainz β†—

Height

#115,501

Difficulty

9.744721

Transactions

2

Size

867 B

Version

2

Bits

09bea602

Nonce

1,517,763

Timestamp

8/13/2013, 7:43:19 PM

Confirmations

6,679,308

Mined by

⛏️ P2SHAWbm4AWfhyZEMkdPYLMs4FyYdBzNGrUw91

Merkle Root

b9b3285d693b69822887b91ca75f233da3b7fa0e856ea575f83224845625c085
Transactions (2)
Coinbase4e15cef25a085a…eb808e23e6d6bd
1 in β†’ 1 out10.5300 XPM109 B
AWbm4AWf…zNGrUw91
6cf8edb61c8a57…00ba54eaca2235
4 in β†’ 2 out23.3719 XPM668 B
AZHGBL9Q…6gU4PaR3AGRxyhKo…5EFv6NYd
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.

9.640 Γ— 10⁹⁴(95-digit number)
96403145200049559266…10512906531915151099
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
9.640 Γ— 10⁹⁴(95-digit number)
96403145200049559266…10512906531915151099
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.640 Γ— 10⁹⁴(95-digit number)
96403145200049559266…10512906531915151101
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
1.928 Γ— 10⁹⁡(96-digit number)
19280629040009911853…21025813063830302199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.928 Γ— 10⁹⁡(96-digit number)
19280629040009911853…21025813063830302201
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
3.856 Γ— 10⁹⁡(96-digit number)
38561258080019823706…42051626127660604399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.856 Γ— 10⁹⁡(96-digit number)
38561258080019823706…42051626127660604401
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
7.712 Γ— 10⁹⁡(96-digit number)
77122516160039647412…84103252255321208799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.712 Γ— 10⁹⁡(96-digit number)
77122516160039647412…84103252255321208801
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
1.542 Γ— 10⁹⁢(97-digit number)
15424503232007929482…68206504510642417599
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:57,602,518 XPMΒ·at block #6,794,808 Β· updates every 60s
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