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Block #74,593

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 11:56:27 AM Β· Difficulty 8.9956 Β· 6,740,441 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f571322e802bd1ebb91145b6a98503107f75846e509c3c4dfd43c3c9538b4032
View on Chainz β†—

Height

#74,593

Difficulty

8.995606

Transactions

1

Size

199 B

Version

2

Bits

08fee003

Nonce

793

Timestamp

7/21/2013, 11:56:27 AM

Confirmations

6,740,441

Mined by

⛏️ P2SHAH7Eh9GYMSnm23owcXVdfkeuiPK86X1CDg

Merkle Root

4f620e227ac883d0197a8e71232d3bed2a044bfcc3ff11fe96c0d9604eff95b6
Transactions (1)
Coinbase4f620e227ac883…c0d9604eff95b6
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.

1.161 Γ— 10⁹³(94-digit number)
11612074120355908016…05044404408905034969
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
1.161 Γ— 10⁹³(94-digit number)
11612074120355908016…05044404408905034969
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.161 Γ— 10⁹³(94-digit number)
11612074120355908016…05044404408905034971
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
2.322 Γ— 10⁹³(94-digit number)
23224148240711816033…10088808817810069939
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.322 Γ— 10⁹³(94-digit number)
23224148240711816033…10088808817810069941
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
4.644 Γ— 10⁹³(94-digit number)
46448296481423632066…20177617635620139879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.644 Γ— 10⁹³(94-digit number)
46448296481423632066…20177617635620139881
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
9.289 Γ— 10⁹³(94-digit number)
92896592962847264133…40355235271240279759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.289 Γ— 10⁹³(94-digit number)
92896592962847264133…40355235271240279761
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
1.857 Γ— 10⁹⁴(95-digit number)
18579318592569452826…80710470542480559519
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:57,764,362 XPMΒ·at block #6,815,033 Β· updates every 60s
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