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Block #2,214,750

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2017, 11:02:44 AM Β· Difficulty 10.9436 Β· 4,624,926 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9837c392f6c9e807e34e299a3685c6a8ec804e0ea9e59b68447de43394b1722a
View on Chainz β†—

Height

#2,214,750

Difficulty

10.943619

Transactions

1

Size

201 B

Version

2

Bits

0af190ff

Nonce

230,947,081

Timestamp

7/20/2017, 11:02:44 AM

Confirmations

4,624,926

Mined by

⛏️ P2SHAVjHU158FZtycTv3QHwtb9oGiHMrbEa21C

Merkle Root

28f1dda74b56e1b3fa0f23ec56dd4662ad2cc4d87c67d81482dacbfdd2fde52a
Transactions (1)
Coinbase28f1dda74b56e1…dacbfdd2fde52a
1 in β†’ 1 out8.3400 XPM110 B
AVjHU158…MrbEa21C
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.

2.761 Γ— 10⁹⁷(98-digit number)
27611869386081195148…52975951005656104959
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
2.761 Γ— 10⁹⁷(98-digit number)
27611869386081195148…52975951005656104959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.761 Γ— 10⁹⁷(98-digit number)
27611869386081195148…52975951005656104961
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
5.522 Γ— 10⁹⁷(98-digit number)
55223738772162390297…05951902011312209919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.522 Γ— 10⁹⁷(98-digit number)
55223738772162390297…05951902011312209921
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
1.104 Γ— 10⁹⁸(99-digit number)
11044747754432478059…11903804022624419839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.104 Γ— 10⁹⁸(99-digit number)
11044747754432478059…11903804022624419841
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
2.208 Γ— 10⁹⁸(99-digit number)
22089495508864956118…23807608045248839679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.208 Γ— 10⁹⁸(99-digit number)
22089495508864956118…23807608045248839681
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
4.417 Γ— 10⁹⁸(99-digit number)
44178991017729912237…47615216090497679359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.417 Γ— 10⁹⁸(99-digit number)
44178991017729912237…47615216090497679361
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
8.835 Γ— 10⁹⁸(99-digit number)
88357982035459824475…95230432180995358719
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:57,961,695 XPMΒ·at block #6,839,675 Β· updates every 60s
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