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Block #2,117,579

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/15/2017, 3:00:30 PM Β· Difficulty 10.9061 Β· 4,725,436 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
188414c0d72c47dd8d6ee2d5a215766f9a9a912e3404582313305da8faecc05a
View on Chainz β†—

Height

#2,117,579

Difficulty

10.906064

Transactions

1

Size

201 B

Version

2

Bits

0ae7f3c9

Nonce

890,318,411

Timestamp

5/15/2017, 3:00:30 PM

Confirmations

4,725,436

Mined by

⛏️ P2SHAd1NMMAdt4KFabiEnJkMo2cWAJbyMCD6x8

Merkle Root

95605e49da5c62908e42a3798d00bc79fa48746292a25199d9cc80964321c700
Transactions (1)
Coinbase95605e49da5c62…cc80964321c700
1 in β†’ 1 out8.3900 XPM110 B
Ad1NMMAd…byMCD6x8
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.

1.382 Γ— 10⁹⁸(99-digit number)
13822609212131585875…00734835281153884159
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
1.382 Γ— 10⁹⁸(99-digit number)
13822609212131585875…00734835281153884159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.382 Γ— 10⁹⁸(99-digit number)
13822609212131585875…00734835281153884161
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
2.764 Γ— 10⁹⁸(99-digit number)
27645218424263171751…01469670562307768319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.764 Γ— 10⁹⁸(99-digit number)
27645218424263171751…01469670562307768321
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
5.529 Γ— 10⁹⁸(99-digit number)
55290436848526343502…02939341124615536639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.529 Γ— 10⁹⁸(99-digit number)
55290436848526343502…02939341124615536641
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
1.105 Γ— 10⁹⁹(100-digit number)
11058087369705268700…05878682249231073279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.105 Γ— 10⁹⁹(100-digit number)
11058087369705268700…05878682249231073281
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
2.211 Γ— 10⁹⁹(100-digit number)
22116174739410537401…11757364498462146559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.211 Γ— 10⁹⁹(100-digit number)
22116174739410537401…11757364498462146561
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
4.423 Γ— 10⁹⁹(100-digit number)
44232349478821074802…23514728996924293119
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
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