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Block #132,798

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/25/2013, 3:34:55 AM Β· Difficulty 9.7907 Β· 6,682,346 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
53031e66f508a6f9b21d25ca064ef4627a8a05615977c19ce6ca824248f42360
View on Chainz β†—

Height

#132,798

Difficulty

9.790730

Transactions

1

Size

201 B

Version

2

Bits

09ca6d49

Nonce

498,003

Timestamp

8/25/2013, 3:34:55 AM

Confirmations

6,682,346

Mined by

⛏️ P2SHAY88KHSTJpyaPqTYGEt3LWdPpt88L8yacq

Merkle Root

5000531c61c8bec378113ce11739725a53cdd6c6068a296009f60f95f086f1e6
Transactions (1)
Coinbase5000531c61c8be…f60f95f086f1e6
1 in β†’ 1 out10.4200 XPM109 B
AY88KHST…88L8yacq
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.

4.625 Γ— 10⁹⁹(100-digit number)
46257775629083725448…26656821928214069319
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
4.625 Γ— 10⁹⁹(100-digit number)
46257775629083725448…26656821928214069319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.625 Γ— 10⁹⁹(100-digit number)
46257775629083725448…26656821928214069321
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
9.251 Γ— 10⁹⁹(100-digit number)
92515551258167450897…53313643856428138639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.251 Γ— 10⁹⁹(100-digit number)
92515551258167450897…53313643856428138641
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
1.850 Γ— 10¹⁰⁰(101-digit number)
18503110251633490179…06627287712856277279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.850 Γ— 10¹⁰⁰(101-digit number)
18503110251633490179…06627287712856277281
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
3.700 Γ— 10¹⁰⁰(101-digit number)
37006220503266980359…13254575425712554559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.700 Γ— 10¹⁰⁰(101-digit number)
37006220503266980359…13254575425712554561
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
7.401 Γ— 10¹⁰⁰(101-digit number)
74012441006533960718…26509150851425109119
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:57,765,246 XPMΒ·at block #6,815,143 Β· updates every 60s
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