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Block #186,094

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/29/2013, 5:20:48 PM Β· Difficulty 9.8642 Β· 6,622,788 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
73579cd5ce511ee8c4b5f3873c03d8c761e7dd99218b522b1da549a49a5d31bf
View on Chainz β†—

Height

#186,094

Difficulty

9.864188

Transactions

1

Size

205 B

Version

2

Bits

09dd3b6a

Nonce

2,992

Timestamp

9/29/2013, 5:20:48 PM

Confirmations

6,622,788

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

a2d087439f1bb51f0a263a5122b6360f5b6ffa56b35e2dbbe2884f5d16d14a46
Transactions (1)
Coinbasea2d087439f1bb5…884f5d16d14a46
1 in β†’ 1 out10.2600 XPM116 B
AcLBm5Z9…S683d7c3
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.

9.604 Γ— 10⁹²(93-digit number)
96049107938731246798…57010695887427073719
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
9.604 Γ— 10⁹²(93-digit number)
96049107938731246798…57010695887427073719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.604 Γ— 10⁹²(93-digit number)
96049107938731246798…57010695887427073721
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
1.920 Γ— 10⁹³(94-digit number)
19209821587746249359…14021391774854147439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.920 Γ— 10⁹³(94-digit number)
19209821587746249359…14021391774854147441
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
3.841 Γ— 10⁹³(94-digit number)
38419643175492498719…28042783549708294879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.841 Γ— 10⁹³(94-digit number)
38419643175492498719…28042783549708294881
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
7.683 Γ— 10⁹³(94-digit number)
76839286350984997438…56085567099416589759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.683 Γ— 10⁹³(94-digit number)
76839286350984997438…56085567099416589761
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
1.536 Γ— 10⁹⁴(95-digit number)
15367857270196999487…12171134198833179519
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:57,715,108 XPMΒ·at block #6,808,881 Β· updates every 60s
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