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Block #89,922

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/30/2013, 5:26:30 PM Β· Difficulty 9.2553 Β· 6,726,710 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
760cfa736de77e80c218f082b0cd4ed79acfc2cbc57a78fb38e7e9e734cc0771
View on Chainz β†—

Height

#89,922

Difficulty

9.255294

Transactions

1

Size

207 B

Version

2

Bits

09415af1

Nonce

1,957,627

Timestamp

7/30/2013, 5:26:30 PM

Confirmations

6,726,710

Mined by

⛏️ P2SHAT5A2KL6kAm5Pa3anhC8W4LVscCT16n6i2

Merkle Root

7aef5adebccc405986247e763b22fddadcb45af5122c9285e6ff82398c15fdaa
Transactions (1)
Coinbase7aef5adebccc40…ff82398c15fdaa
1 in β†’ 1 out11.6600 XPM112 B
AT5A2KL6…CT16n6i2
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.

2.475 Γ— 10¹⁰⁷(108-digit number)
24752745718805719251…88931060602314446869
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
2.475 Γ— 10¹⁰⁷(108-digit number)
24752745718805719251…88931060602314446869
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.475 Γ— 10¹⁰⁷(108-digit number)
24752745718805719251…88931060602314446871
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
4.950 Γ— 10¹⁰⁷(108-digit number)
49505491437611438503…77862121204628893739
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.950 Γ— 10¹⁰⁷(108-digit number)
49505491437611438503…77862121204628893741
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
9.901 Γ— 10¹⁰⁷(108-digit number)
99010982875222877007…55724242409257787479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.901 Γ— 10¹⁰⁷(108-digit number)
99010982875222877007…55724242409257787481
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
1.980 Γ— 10¹⁰⁸(109-digit number)
19802196575044575401…11448484818515574959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.980 Γ— 10¹⁰⁸(109-digit number)
19802196575044575401…11448484818515574961
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
3.960 Γ— 10¹⁰⁸(109-digit number)
39604393150089150802…22896969637031149919
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:57,777,170 XPMΒ·at block #6,816,631 Β· updates every 60s
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