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Block #2,129,123

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/23/2017, 10:49:13 AM Β· Difficulty 10.9115 Β· 4,711,756 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ae86d9227d4fc00105aecf2f182252fbdb7a31184cf37e3eac75457f0c3c83a8
View on Chainz β†—

Height

#2,129,123

Difficulty

10.911480

Transactions

2

Size

424 B

Version

2

Bits

0ae956c1

Nonce

612,182,862

Timestamp

5/23/2017, 10:49:13 AM

Confirmations

4,711,756

Mined by

⛏️ P2SHALjpxmcXboqsiNHEF3N9Z4gGAvAeqPs3fp

Merkle Root

9a23fe5a521aecc65c81b9146dff1bbccd3589a0ff7414c0441ce9722a50c5f9
Transactions (2)
Coinbased97a0eb127874a…f347b1e48a7cff
1 in β†’ 1 out8.4000 XPM109 B
ALjpxmcX…AeqPs3fp
30ab278bac0775…b9a95807250ccc
1 in β†’ 2 out19.7900 XPM225 B
AQyp7UE7…syd6HSdCAKTddAdL…Ta8uprGd
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.

2.001 Γ— 10⁹⁴(95-digit number)
20012357789964484958…76686657786789095999
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
2.001 Γ— 10⁹⁴(95-digit number)
20012357789964484958…76686657786789095999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.001 Γ— 10⁹⁴(95-digit number)
20012357789964484958…76686657786789096001
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
4.002 Γ— 10⁹⁴(95-digit number)
40024715579928969916…53373315573578191999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.002 Γ— 10⁹⁴(95-digit number)
40024715579928969916…53373315573578192001
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
8.004 Γ— 10⁹⁴(95-digit number)
80049431159857939832…06746631147156383999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.004 Γ— 10⁹⁴(95-digit number)
80049431159857939832…06746631147156384001
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
1.600 Γ— 10⁹⁡(96-digit number)
16009886231971587966…13493262294312767999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.600 Γ— 10⁹⁡(96-digit number)
16009886231971587966…13493262294312768001
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
3.201 Γ— 10⁹⁡(96-digit number)
32019772463943175932…26986524588625535999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.201 Γ— 10⁹⁡(96-digit number)
32019772463943175932…26986524588625536001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.403 Γ— 10⁹⁡(96-digit number)
64039544927886351865…53973049177251071999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,971,380 XPMΒ·at block #6,840,878 Β· updates every 60s
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