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Block #452,920

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/20/2014, 9:47:08 PM Β· Difficulty 10.3941 Β· 6,363,903 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ec4ac8077f5a1b13d8866f4ced500fc89d263b594b866710f7c734d15f411eb6
View on Chainz β†—

Height

#452,920

Difficulty

10.394075

Transactions

3

Size

582 B

Version

2

Bits

0a64e21b

Nonce

14,720,819

Timestamp

3/20/2014, 9:47:08 PM

Confirmations

6,363,903

Mined by

⛏️ P2SHAeyaZY4ZULPnUA7HcAzV2c4t8qJ5FfQ4ts

Merkle Root

345b5f2e595231be3f8f139e18b38ed6735a8d32862d8045d683fa5981161f90
Transactions (3)
Coinbasee371dcfb202df6…2d35d8324cad08
1 in β†’ 1 out9.2682 XPM109 B
AeyaZY4Z…J5FfQ4ts
ff72ac365b246a…965ab8d96d839a
1 in β†’ 1 out3.0300 XPM191 B
AbgaVzFq…nHESxhpC
930a114dbd8a36…336a04cbc83b73
1 in β†’ 1 out1.0300 XPM192 B
AUC8qpT3…zzD6FZvv
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.

3.454 Γ— 10⁹⁡(96-digit number)
34548227284844507397…56646091663490182399
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
3.454 Γ— 10⁹⁡(96-digit number)
34548227284844507397…56646091663490182399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.454 Γ— 10⁹⁡(96-digit number)
34548227284844507397…56646091663490182401
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
6.909 Γ— 10⁹⁡(96-digit number)
69096454569689014794…13292183326980364799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.909 Γ— 10⁹⁡(96-digit number)
69096454569689014794…13292183326980364801
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
1.381 Γ— 10⁹⁢(97-digit number)
13819290913937802958…26584366653960729599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.381 Γ— 10⁹⁢(97-digit number)
13819290913937802958…26584366653960729601
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
2.763 Γ— 10⁹⁢(97-digit number)
27638581827875605917…53168733307921459199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.763 Γ— 10⁹⁢(97-digit number)
27638581827875605917…53168733307921459201
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
5.527 Γ— 10⁹⁢(97-digit number)
55277163655751211835…06337466615842918399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.527 Γ— 10⁹⁢(97-digit number)
55277163655751211835…06337466615842918401
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:57,778,623 XPMΒ·at block #6,816,822 Β· updates every 60s
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