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Block #150,450

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2013, 1:08:15 AM Β· Difficulty 9.8587 Β· 6,657,658 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fc86b8b2a1e86c1acc8882bffed8e4ece30371e2750150fb5005a54b6f7e7e21
View on Chainz β†—

Height

#150,450

Difficulty

9.858718

Transactions

1

Size

198 B

Version

2

Bits

09dbd4ee

Nonce

55,364

Timestamp

9/5/2013, 1:08:15 AM

Confirmations

6,657,658

Mined by

⛏️ P2SHAP91QEDQfufBUohT6sogfnRJN9W6JZAB9n

Merkle Root

e0c3ca15a4f1583187df14e128c4b1482341682b10078cbceb5a8d870b7cbeb6
Transactions (1)
Coinbasee0c3ca15a4f158…5a8d870b7cbeb6
1 in β†’ 1 out10.2700 XPM109 B
AP91QEDQ…W6JZAB9n
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.

2.517 Γ— 10⁹³(94-digit number)
25174355618000743561…60545040222409626239
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
2.517 Γ— 10⁹³(94-digit number)
25174355618000743561…60545040222409626239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.517 Γ— 10⁹³(94-digit number)
25174355618000743561…60545040222409626241
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
5.034 Γ— 10⁹³(94-digit number)
50348711236001487122…21090080444819252479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.034 Γ— 10⁹³(94-digit number)
50348711236001487122…21090080444819252481
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
1.006 Γ— 10⁹⁴(95-digit number)
10069742247200297424…42180160889638504959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.006 Γ— 10⁹⁴(95-digit number)
10069742247200297424…42180160889638504961
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
2.013 Γ— 10⁹⁴(95-digit number)
20139484494400594849…84360321779277009919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.013 Γ— 10⁹⁴(95-digit number)
20139484494400594849…84360321779277009921
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
4.027 Γ— 10⁹⁴(95-digit number)
40278968988801189698…68720643558554019839
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:57,708,911 XPMΒ·at block #6,808,107 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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