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Block #343,119

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/4/2014, 12:11:50 PM Β· Difficulty 10.1682 Β· 6,473,658 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
776d255aaf906cf106c4732cdc6afa4664521cfde39a72ab0ae293a61989ca5b
View on Chainz β†—

Height

#343,119

Difficulty

10.168158

Transactions

1

Size

200 B

Version

2

Bits

0a2b0c6b

Nonce

18,243

Timestamp

1/4/2014, 12:11:50 PM

Confirmations

6,473,658

Mined by

⛏️ P2SHAGFq49aSk3FXbxq7WttNzWezyjSD3NMsx7

Merkle Root

e23d4173f0a04627015f49ba49f1a62067b408f4e97acfb9e2e5c5b7047c946e
Transactions (1)
Coinbasee23d4173f0a046…e5c5b7047c946e
1 in β†’ 1 out9.6600 XPM109 B
AGFq49aS…SD3NMsx7
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.

9.015 Γ— 10⁹⁷(98-digit number)
90156996870524106559…04263172717070033119
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
9.015 Γ— 10⁹⁷(98-digit number)
90156996870524106559…04263172717070033119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.015 Γ— 10⁹⁷(98-digit number)
90156996870524106559…04263172717070033121
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
1.803 Γ— 10⁹⁸(99-digit number)
18031399374104821311…08526345434140066239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.803 Γ— 10⁹⁸(99-digit number)
18031399374104821311…08526345434140066241
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
3.606 Γ— 10⁹⁸(99-digit number)
36062798748209642623…17052690868280132479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.606 Γ— 10⁹⁸(99-digit number)
36062798748209642623…17052690868280132481
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
7.212 Γ— 10⁹⁸(99-digit number)
72125597496419285247…34105381736560264959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.212 Γ— 10⁹⁸(99-digit number)
72125597496419285247…34105381736560264961
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
1.442 Γ— 10⁹⁹(100-digit number)
14425119499283857049…68210763473120529919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.442 Γ— 10⁹⁹(100-digit number)
14425119499283857049…68210763473120529921
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:57,778,250 XPMΒ·at block #6,816,776 Β· updates every 60s
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