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Block #232,987

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/29/2013, 10:54:56 AM Β· Difficulty 9.9419 Β· 6,571,172 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6c7a4af17abc89cf5ae717eb18bdddb71d98f0bcde3a90bd8aad42f95180711a
View on Chainz β†—

Height

#232,987

Difficulty

9.941917

Transactions

1

Size

201 B

Version

2

Bits

09f1217b

Nonce

52,029

Timestamp

10/29/2013, 10:54:56 AM

Confirmations

6,571,172

Mined by

⛏️ P2SHAH8MuWecApb7HmsNwfd9UPDw7y2bVG62mK

Merkle Root

094fa57b042078a5ad87c62ff17698219113b1583e515d51f9f36f5dc3ae964d
Transactions (1)
Coinbase094fa57b042078…f36f5dc3ae964d
1 in β†’ 1 out10.1000 XPM109 B
AH8MuWec…2bVG62mK
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.

1.782 Γ— 10¹⁰⁰(101-digit number)
17826044228232190935…98290958676342259199
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
1.782 Γ— 10¹⁰⁰(101-digit number)
17826044228232190935…98290958676342259199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.782 Γ— 10¹⁰⁰(101-digit number)
17826044228232190935…98290958676342259201
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
3.565 Γ— 10¹⁰⁰(101-digit number)
35652088456464381871…96581917352684518399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.565 Γ— 10¹⁰⁰(101-digit number)
35652088456464381871…96581917352684518401
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
7.130 Γ— 10¹⁰⁰(101-digit number)
71304176912928763742…93163834705369036799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.130 Γ— 10¹⁰⁰(101-digit number)
71304176912928763742…93163834705369036801
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
1.426 Γ— 10¹⁰¹(102-digit number)
14260835382585752748…86327669410738073599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.426 Γ— 10¹⁰¹(102-digit number)
14260835382585752748…86327669410738073601
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
2.852 Γ— 10¹⁰¹(102-digit number)
28521670765171505496…72655338821476147199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.852 Γ— 10¹⁰¹(102-digit number)
28521670765171505496…72655338821476147201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,677,325 XPMΒ·at block #6,804,158 Β· updates every 60s
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