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Block #2,800,678

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/19/2018, 11:54:30 AM Β· Difficulty 11.6713 Β· 4,039,932 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d5fd690224e2d0c62d91d842330b1b5f20afca22fc9d3f1c1a7c3edd085a6cf8
View on Chainz β†—

Height

#2,800,678

Difficulty

11.671330

Transactions

3

Size

949 B

Version

2

Bits

0babdc48

Nonce

470,757,337

Timestamp

8/19/2018, 11:54:30 AM

Confirmations

4,039,932

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

0411ee3d925af76810181fe6393343c44fc62b6e8aa648837647d1830fdbaeca
Transactions (3)
Coinbasec569e9db32aa47…99c9678a91547f
1 in β†’ 1 out7.3500 XPM110 B
AZtxQr2F…7grUWrUz
a86d4b1f2831a8…504e5097dcffb1
1 in β†’ 2 out3.2037 XPM225 B
ANjTQp24…sVkz8XupAcy4GhSh…oH4kZq2E
be9c9389934a1c…4f20be9ebf87ce
3 in β†’ 2 out4.0795 XPM523 B
AcYH6cQc…csrAU8nXAJk76m7n…5c12ta2b
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.

3.186 Γ— 10⁹⁢(97-digit number)
31867770429665799027…11426641992808017919
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
3.186 Γ— 10⁹⁢(97-digit number)
31867770429665799027…11426641992808017919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.186 Γ— 10⁹⁢(97-digit number)
31867770429665799027…11426641992808017921
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
6.373 Γ— 10⁹⁢(97-digit number)
63735540859331598054…22853283985616035839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.373 Γ— 10⁹⁢(97-digit number)
63735540859331598054…22853283985616035841
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
1.274 Γ— 10⁹⁷(98-digit number)
12747108171866319610…45706567971232071679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.274 Γ— 10⁹⁷(98-digit number)
12747108171866319610…45706567971232071681
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
2.549 Γ— 10⁹⁷(98-digit number)
25494216343732639221…91413135942464143359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.549 Γ— 10⁹⁷(98-digit number)
25494216343732639221…91413135942464143361
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
5.098 Γ— 10⁹⁷(98-digit number)
50988432687465278443…82826271884928286719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.098 Γ— 10⁹⁷(98-digit number)
50988432687465278443…82826271884928286721
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
1.019 Γ— 10⁹⁸(99-digit number)
10197686537493055688…65652543769856573439
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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