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Block #141,873

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/30/2013, 2:51:59 PM Β· Difficulty 9.8352 Β· 6,682,650 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fc35fee62fcd0b125e2fc3717db399f5c587477b73befe43cfa16cc7cc6cce20
View on Chainz β†—

Height

#141,873

Difficulty

9.835249

Transactions

1

Size

199 B

Version

2

Bits

09d5d2db

Nonce

11,008

Timestamp

8/30/2013, 2:51:59 PM

Confirmations

6,682,650

Mined by

⛏️ P2SHAP52EE3FezHothJTJo3Xw2Hi1LZhqfNP3e

Merkle Root

7a01e78acf4f08ef495d149014b72dea10e1af8358b09f07b8753f536950796f
Transactions (1)
Coinbase7a01e78acf4f08…753f536950796f
1 in β†’ 1 out10.3200 XPM109 B
AP52EE3F…ZhqfNP3e
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.

6.372 Γ— 10⁹⁡(96-digit number)
63727784538786034530…59977927636673240239
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
6.372 Γ— 10⁹⁡(96-digit number)
63727784538786034530…59977927636673240239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.372 Γ— 10⁹⁡(96-digit number)
63727784538786034530…59977927636673240241
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
1.274 Γ— 10⁹⁢(97-digit number)
12745556907757206906…19955855273346480479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.274 Γ— 10⁹⁢(97-digit number)
12745556907757206906…19955855273346480481
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
2.549 Γ— 10⁹⁢(97-digit number)
25491113815514413812…39911710546692960959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.549 Γ— 10⁹⁢(97-digit number)
25491113815514413812…39911710546692960961
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
5.098 Γ— 10⁹⁢(97-digit number)
50982227631028827624…79823421093385921919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.098 Γ— 10⁹⁢(97-digit number)
50982227631028827624…79823421093385921921
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
1.019 Γ— 10⁹⁷(98-digit number)
10196445526205765524…59646842186771843839
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:57,840,247 XPMΒ·at block #6,824,522 Β· updates every 60s
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