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Block #50,826

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/16/2013, 3:07:22 AM Β· Difficulty 8.8889 Β· 6,744,693 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5809ff6540e427fbd9ff1a7ec3e3ccaccb45a951fd28714c3cca3cce909e6bb6
View on Chainz β†—

Height

#50,826

Difficulty

8.888899

Transactions

2

Size

355 B

Version

2

Bits

08e38ee9

Nonce

209

Timestamp

7/16/2013, 3:07:22 AM

Confirmations

6,744,693

Mined by

⛏️ P2SHAVpGk3q8PHXaJqCaTV3HNvPJfx3tMZhgzZ

Merkle Root

e4b30fc7f135353420fad21a2f9321db3afeb500fd9c731e46625e801207d0e2
Transactions (2)
Coinbaseada1397870843c…104cf073df27b9
1 in β†’ 1 out12.6500 XPM110 B
AVpGk3q8…3tMZhgzZ
3539574cfdb040…afa05a27587ec6
1 in β†’ 1 out12.8300 XPM158 B
AU4AxAzL…y8DH19oQ
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.

5.781 Γ— 10⁸⁢(87-digit number)
57813407084730701415…34785477287959148219
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
5.781 Γ— 10⁸⁢(87-digit number)
57813407084730701415…34785477287959148219
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.781 Γ— 10⁸⁢(87-digit number)
57813407084730701415…34785477287959148221
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
1.156 Γ— 10⁸⁷(88-digit number)
11562681416946140283…69570954575918296439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.156 Γ— 10⁸⁷(88-digit number)
11562681416946140283…69570954575918296441
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
2.312 Γ— 10⁸⁷(88-digit number)
23125362833892280566…39141909151836592879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.312 Γ— 10⁸⁷(88-digit number)
23125362833892280566…39141909151836592881
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
4.625 Γ— 10⁸⁷(88-digit number)
46250725667784561132…78283818303673185759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.625 Γ— 10⁸⁷(88-digit number)
46250725667784561132…78283818303673185761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,608,213 XPMΒ·at block #6,795,518 Β· updates every 60s
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