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Block #151,420

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2013, 4:23:15 PM Β· Difficulty 9.8603 Β· 6,662,704 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
320173830e38a5d5e996227f716a7c8f2802b742a2f3ca8562fdce10a6cc830e
View on Chainz β†—

Height

#151,420

Difficulty

9.860290

Transactions

1

Size

200 B

Version

2

Bits

09dc3bf4

Nonce

38,143

Timestamp

9/5/2013, 4:23:15 PM

Confirmations

6,662,704

Mined by

⛏️ P2SHAKtBx3MqZ6vNPRGj8sjbxpXkoF79Vfynvn

Merkle Root

df1e91eed7f7f1614b37e623518dfc7c659cf12ec0c2d8efac57c020642bb20c
Transactions (1)
Coinbasedf1e91eed7f7f1…57c020642bb20c
1 in β†’ 1 out10.2700 XPM109 B
AKtBx3Mq…79Vfynvn
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.

7.608 Γ— 10⁹⁢(97-digit number)
76084872497650029541…15775873322930204159
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
7.608 Γ— 10⁹⁢(97-digit number)
76084872497650029541…15775873322930204159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.608 Γ— 10⁹⁢(97-digit number)
76084872497650029541…15775873322930204161
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
1.521 Γ— 10⁹⁷(98-digit number)
15216974499530005908…31551746645860408319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.521 Γ— 10⁹⁷(98-digit number)
15216974499530005908…31551746645860408321
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
3.043 Γ— 10⁹⁷(98-digit number)
30433948999060011816…63103493291720816639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.043 Γ— 10⁹⁷(98-digit number)
30433948999060011816…63103493291720816641
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
6.086 Γ— 10⁹⁷(98-digit number)
60867897998120023633…26206986583441633279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.086 Γ— 10⁹⁷(98-digit number)
60867897998120023633…26206986583441633281
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
1.217 Γ— 10⁹⁸(99-digit number)
12173579599624004726…52413973166883266559
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:57,757,076 XPMΒ·at block #6,814,123 Β· updates every 60s
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