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Block #159,941

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/11/2013, 1:06:56 PM Β· Difficulty 9.8627 Β· 6,634,767 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
16f47fe9d896e6e48e86857eea2b4e25c66750097361b52d0a4c02e7a21bacf4
View on Chainz β†—

Height

#159,941

Difficulty

9.862730

Transactions

1

Size

199 B

Version

2

Bits

09dcdbdb

Nonce

46,383

Timestamp

9/11/2013, 1:06:56 PM

Confirmations

6,634,767

Mined by

⛏️ P2SHAcrXkx8MtAxrjWsXe8rTH4v6wMtKGb6K4t

Merkle Root

ee44043bdace71a57bf32cc87dd832fa4ce34bd9a621881f929e7eec672841ec
Transactions (1)
Coinbaseee44043bdace71…9e7eec672841ec
1 in β†’ 1 out10.2700 XPM109 B
AcrXkx8M…tKGb6K4t
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.

5.213 Γ— 10⁹³(94-digit number)
52130467809188942621…58003754916391864319
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
5.213 Γ— 10⁹³(94-digit number)
52130467809188942621…58003754916391864319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.213 Γ— 10⁹³(94-digit number)
52130467809188942621…58003754916391864321
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
1.042 Γ— 10⁹⁴(95-digit number)
10426093561837788524…16007509832783728639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.042 Γ— 10⁹⁴(95-digit number)
10426093561837788524…16007509832783728641
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
2.085 Γ— 10⁹⁴(95-digit number)
20852187123675577048…32015019665567457279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.085 Γ— 10⁹⁴(95-digit number)
20852187123675577048…32015019665567457281
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
4.170 Γ— 10⁹⁴(95-digit number)
41704374247351154097…64030039331134914559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.170 Γ— 10⁹⁴(95-digit number)
41704374247351154097…64030039331134914561
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
8.340 Γ— 10⁹⁴(95-digit number)
83408748494702308194…28060078662269829119
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:57,601,711 XPMΒ·at block #6,794,707 Β· updates every 60s
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