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Block #370,975

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/22/2014, 12:49:41 PM Β· Difficulty 10.4375 Β· 6,438,545 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f19a063b4fd65d278f72f1516c00a5d3a163d40b14655d16350a0e7b0781c74b
View on Chainz β†—

Height

#370,975

Difficulty

10.437541

Transactions

1

Size

207 B

Version

2

Bits

0a7002b3

Nonce

19,520

Timestamp

1/22/2014, 12:49:41 PM

Confirmations

6,438,545

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

635969a61f47595471434125fc66df79aa3b2b622816b008779aa7f41bd52fe9
Transactions (1)
Coinbase635969a61f4759…9aa7f41bd52fe9
1 in β†’ 1 out9.1600 XPM116 B
AbwWkWZt…kawDhufa
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.

3.831 Γ— 10⁹⁷(98-digit number)
38310844537857348038…81189033047412661389
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
3.831 Γ— 10⁹⁷(98-digit number)
38310844537857348038…81189033047412661389
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.831 Γ— 10⁹⁷(98-digit number)
38310844537857348038…81189033047412661391
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
7.662 Γ— 10⁹⁷(98-digit number)
76621689075714696077…62378066094825322779
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.662 Γ— 10⁹⁷(98-digit number)
76621689075714696077…62378066094825322781
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
1.532 Γ— 10⁹⁸(99-digit number)
15324337815142939215…24756132189650645559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.532 Γ— 10⁹⁸(99-digit number)
15324337815142939215…24756132189650645561
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
3.064 Γ— 10⁹⁸(99-digit number)
30648675630285878431…49512264379301291119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.064 Γ— 10⁹⁸(99-digit number)
30648675630285878431…49512264379301291121
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
6.129 Γ— 10⁹⁸(99-digit number)
61297351260571756862…99024528758602582239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.129 Γ— 10⁹⁸(99-digit number)
61297351260571756862…99024528758602582241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,720,236 XPMΒ·at block #6,809,519 Β· updates every 60s
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