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Block #963,774

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/6/2015, 1:25:19 PM Β· Difficulty 10.8772 Β· 5,831,278 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
adaebfdcecc23e0e37827a57d52a2b8295c9fd3d1e2b38dd397177fcae3ee1c8
View on Chainz β†—

Height

#963,774

Difficulty

10.877161

Transactions

2

Size

1.14 KB

Version

2

Bits

0ae08d98

Nonce

1,012,005,697

Timestamp

3/6/2015, 1:25:19 PM

Confirmations

5,831,278

Mined by

⛏️ P2SHAddqFU1VgUaoM9dVsKfXHhgJj58UdNBTWS

Merkle Root

0666c37692e7dec832888ee70818c07af39fd88b11cb721237fb8e6e13c72e6b
Transactions (2)
Coinbasec00aa6740d71b1…9f67d4e89807e7
1 in β†’ 1 out8.4600 XPM109 B
AddqFU1V…8UdNBTWS
48ba39fa5d4a74…4ed3edaf32db39
6 in β†’ 2 out929.3105 XPM965 B
AJC3S6fs…QhsVcztJAPKirZWi…NTdN7ZTc
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.

5.470 Γ— 10⁹⁴(95-digit number)
54700644539964661088…13723734411545036799
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
5.470 Γ— 10⁹⁴(95-digit number)
54700644539964661088…13723734411545036799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.470 Γ— 10⁹⁴(95-digit number)
54700644539964661088…13723734411545036801
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
1.094 Γ— 10⁹⁡(96-digit number)
10940128907992932217…27447468823090073599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.094 Γ— 10⁹⁡(96-digit number)
10940128907992932217…27447468823090073601
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
2.188 Γ— 10⁹⁡(96-digit number)
21880257815985864435…54894937646180147199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.188 Γ— 10⁹⁡(96-digit number)
21880257815985864435…54894937646180147201
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
4.376 Γ— 10⁹⁡(96-digit number)
43760515631971728870…09789875292360294399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.376 Γ— 10⁹⁡(96-digit number)
43760515631971728870…09789875292360294401
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
8.752 Γ— 10⁹⁡(96-digit number)
87521031263943457741…19579750584720588799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.752 Γ— 10⁹⁡(96-digit number)
87521031263943457741…19579750584720588801
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
1.750 Γ— 10⁹⁢(97-digit number)
17504206252788691548…39159501169441177599
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:57,604,456 XPMΒ·at block #6,795,051 Β· updates every 60s
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