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Block #2,114,952

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/13/2017, 11:36:48 PM Β· Difficulty 10.9009 Β· 4,701,594 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9e5812beacef1f69eb4f836964e31a428aa90530c5e3b18519f6264d7f173b2e
View on Chainz β†—

Height

#2,114,952

Difficulty

10.900947

Transactions

2

Size

2.98 KB

Version

2

Bits

0ae6a47b

Nonce

804,865,008

Timestamp

5/13/2017, 11:36:48 PM

Confirmations

4,701,594

Mined by

⛏️ P2SHAMCzggdWHkWLusYkWU6pYaBqvU1mBp6aKD

Merkle Root

38e3d381aec7300554e22e3fff25fb42ea6fc47f60a6e992d36b3b3c8602a3af
Transactions (2)
Coinbase31d302d556f1e8…80f28c0a167510
1 in β†’ 1 out8.4300 XPM110 B
AMCzggdW…1mBp6aKD
9df59369061fc8…0728dac16752e8
19 in β†’ 1 out2952.9900 XPM2.79 KB
AKc8GdcV…PFmVnxov
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.

7.263 Γ— 10⁹⁴(95-digit number)
72631310070279042913…66625483295312550719
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
7.263 Γ— 10⁹⁴(95-digit number)
72631310070279042913…66625483295312550719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.263 Γ— 10⁹⁴(95-digit number)
72631310070279042913…66625483295312550721
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
1.452 Γ— 10⁹⁡(96-digit number)
14526262014055808582…33250966590625101439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.452 Γ— 10⁹⁡(96-digit number)
14526262014055808582…33250966590625101441
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
2.905 Γ— 10⁹⁡(96-digit number)
29052524028111617165…66501933181250202879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.905 Γ— 10⁹⁡(96-digit number)
29052524028111617165…66501933181250202881
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
5.810 Γ— 10⁹⁡(96-digit number)
58105048056223234330…33003866362500405759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.810 Γ— 10⁹⁡(96-digit number)
58105048056223234330…33003866362500405761
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
1.162 Γ— 10⁹⁢(97-digit number)
11621009611244646866…66007732725000811519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.162 Γ— 10⁹⁢(97-digit number)
11621009611244646866…66007732725000811521
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:57,776,497 XPMΒ·at block #6,816,545 Β· updates every 60s
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