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Block #2,468,510

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/11/2018, 8:58:27 PM Β· Difficulty 10.9602 Β· 4,370,609 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1b55d505a73c58ed6792abf83c79d1abe884ef60c9e906a5dcf3fe2ef0c50edc
View on Chainz β†—

Height

#2,468,510

Difficulty

10.960155

Transactions

2

Size

719 B

Version

2

Bits

0af5ccb0

Nonce

283,038,616

Timestamp

1/11/2018, 8:58:27 PM

Confirmations

4,370,609

Mined by

⛏️ P2SHAXLT9jZGkRNC7RB5qvXc8GdnwsVoKLJL9q

Merkle Root

98d9dec34fef00193f9a3cff591189441c4972b68b10dfc2025d8d6555784b1a
Transactions (2)
Coinbaseb41149f5cf6ac4…e0071787e2bb90
1 in β†’ 1 out8.3200 XPM109 B
AXLT9jZG…VoKLJL9q
808303dd1ddc61…1ba10d28385a68
3 in β†’ 2 out462.4550 XPM519 B
AHh4bPJP…4AwtSb7WAK7gaE3M…Etr26wz3
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.

7.413 Γ— 10⁹⁡(96-digit number)
74133934730207983296…97024946315564348159
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
7.413 Γ— 10⁹⁡(96-digit number)
74133934730207983296…97024946315564348159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.413 Γ— 10⁹⁡(96-digit number)
74133934730207983296…97024946315564348161
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
1.482 Γ— 10⁹⁢(97-digit number)
14826786946041596659…94049892631128696319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.482 Γ— 10⁹⁢(97-digit number)
14826786946041596659…94049892631128696321
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
2.965 Γ— 10⁹⁢(97-digit number)
29653573892083193318…88099785262257392639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.965 Γ— 10⁹⁢(97-digit number)
29653573892083193318…88099785262257392641
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
5.930 Γ— 10⁹⁢(97-digit number)
59307147784166386637…76199570524514785279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.930 Γ— 10⁹⁢(97-digit number)
59307147784166386637…76199570524514785281
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
1.186 Γ— 10⁹⁷(98-digit number)
11861429556833277327…52399141049029570559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.186 Γ— 10⁹⁷(98-digit number)
11861429556833277327…52399141049029570561
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
2.372 Γ— 10⁹⁷(98-digit number)
23722859113666554654…04798282098059141119
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:57,957,227 XPMΒ·at block #6,839,118 Β· updates every 60s
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