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Block #161,831

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/12/2013, 10:07:44 PM Β· Difficulty 9.8603 Β· 6,645,971 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1a549e16d397c5bc1282762e758abb26da9f46484a5deb9006092616fcb8374b
View on Chainz β†—

Height

#161,831

Difficulty

9.860342

Transactions

1

Size

198 B

Version

2

Bits

09dc3f5a

Nonce

38,223

Timestamp

9/12/2013, 10:07:44 PM

Confirmations

6,645,971

Mined by

⛏️ P2SHAWbm4AWfhyZEMkdPYLMs4FyYdBzNGrUw91

Merkle Root

66370dab8b365f7285ceb2c1d5ab2b542599d207454a8983d7d981705ea1f1a9
Transactions (1)
Coinbase66370dab8b365f…d981705ea1f1a9
1 in β†’ 1 out10.2700 XPM109 B
AWbm4AWf…zNGrUw91
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.

8.655 Γ— 10⁹¹(92-digit number)
86551441220432848859…14634302618546590359
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
8.655 Γ— 10⁹¹(92-digit number)
86551441220432848859…14634302618546590359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.655 Γ— 10⁹¹(92-digit number)
86551441220432848859…14634302618546590361
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
1.731 Γ— 10⁹²(93-digit number)
17310288244086569771…29268605237093180719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.731 Γ— 10⁹²(93-digit number)
17310288244086569771…29268605237093180721
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
3.462 Γ— 10⁹²(93-digit number)
34620576488173139543…58537210474186361439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.462 Γ— 10⁹²(93-digit number)
34620576488173139543…58537210474186361441
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
6.924 Γ— 10⁹²(93-digit number)
69241152976346279087…17074420948372722879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.924 Γ— 10⁹²(93-digit number)
69241152976346279087…17074420948372722881
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
1.384 Γ— 10⁹³(94-digit number)
13848230595269255817…34148841896745445759
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:57,706,450 XPMΒ·at block #6,807,801 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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