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Block #181,750

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/26/2013, 6:53:49 PM Β· Difficulty 9.8576 Β· 6,632,640 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0e6a1e60230ab87f15ddfbd4318ad6a4130cf3226eb9e9d2800b37c8d6a1d7ad
View on Chainz β†—

Height

#181,750

Difficulty

9.857633

Transactions

1

Size

201 B

Version

2

Bits

09db8ddc

Nonce

64,374

Timestamp

9/26/2013, 6:53:49 PM

Confirmations

6,632,640

Mined by

⛏️ P2SHAWbQMT1UFX9Fb1nejhFo5DMbcK8Pt4ow7J

Merkle Root

d927b36441622529f2fa9a37bc1f6e21ce0b27f1a29f42e4463b2726f1cede9f
Transactions (1)
Coinbased927b364416225…3b2726f1cede9f
1 in β†’ 1 out10.2800 XPM109 B
AWbQMT1U…8Pt4ow7J
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.

2.326 Γ— 10¹⁰⁰(101-digit number)
23267830761443247161…41497113054473338879
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
2.326 Γ— 10¹⁰⁰(101-digit number)
23267830761443247161…41497113054473338879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.326 Γ— 10¹⁰⁰(101-digit number)
23267830761443247161…41497113054473338881
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
4.653 Γ— 10¹⁰⁰(101-digit number)
46535661522886494323…82994226108946677759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.653 Γ— 10¹⁰⁰(101-digit number)
46535661522886494323…82994226108946677761
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
9.307 Γ— 10¹⁰⁰(101-digit number)
93071323045772988647…65988452217893355519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.307 Γ— 10¹⁰⁰(101-digit number)
93071323045772988647…65988452217893355521
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
1.861 Γ— 10¹⁰¹(102-digit number)
18614264609154597729…31976904435786711039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.861 Γ— 10¹⁰¹(102-digit number)
18614264609154597729…31976904435786711041
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
3.722 Γ— 10¹⁰¹(102-digit number)
37228529218309195459…63953808871573422079
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:57,759,181 XPMΒ·at block #6,814,389 Β· updates every 60s
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